US7701804B2 - Method and constructing a model of a heterogeneous medium described by several parameters from data expressed in different time scales - Google Patents
Method and constructing a model of a heterogeneous medium described by several parameters from data expressed in different time scales Download PDFInfo
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- US7701804B2 US7701804B2 US11/194,528 US19452805A US7701804B2 US 7701804 B2 US7701804 B2 US 7701804B2 US 19452805 A US19452805 A US 19452805A US 7701804 B2 US7701804 B2 US 7701804B2
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
- G01V1/00—Seismology; Seismic or acoustic prospecting or detecting
- G01V1/28—Processing seismic data, e.g. analysis, for interpretation, for correction
- G01V1/30—Analysis
- G01V1/301—Analysis for determining seismic cross-sections or geostructures
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
- G01V1/00—Seismology; Seismic or acoustic prospecting or detecting
- G01V1/28—Processing seismic data, e.g. analysis, for interpretation, for correction
- G01V1/284—Application of the shear wave component and/or several components of the seismic signal
Abstract
Description
- Aki, K., and Richards, P. G., 1980, Quantitative Seismology: Theory and Method, Vol.1: W.H. Freeman and Co
- De Nicolao, A., Drufuca, G., and Rocca, F., 1993, Eigenvalues and eigenvectors of Linearized Elastic Inversion: Geophysics, 58, 670-679.
- Gaiser, J. E., 1996, Multicomponent Vp/Vs Correlation Analysis: Geophysics, 61, 1137-1149.
- Garotta, R., Granger, P-Y., and Dariu, H., 2000, Elastic Parameter Derivations from Multi-component Data, 70th Ann. Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts, 154-157.
- Lebrun, D., Richard, V., Mace, D., and Cuer, M., 2001, SVD for Multi-Offset Linearized Inversion: Resolution Analysis in Multicomponent Acquisition: Geophysics, 66, 871-882.
- Tonellot, T., Macé, D., Richard, V., and Cuer, M., 2001, Joint Stratigraphic Inversion of Angle-Limited Stacks, 71th Ann. Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts, 227-230.
is the best determined parameter from the PP data; on the other hand, the confidence that one can have in the relative variation of the S impedance is more limited and depends on factors such as the noise level, the range of incidence angles available and the errors on determination of the velocity model. However, if PS data are available, it is possible to reliably estimate the relative variation of the S impedance, hence an ever-growing interest in the acquisition and processing of multicomponent seismic data. As for density, it is difficult to estimate whatever the type of data used.
- the ordinate at the PP origin, referred to as PP “intercept” and expressed in PP time,
- the PP “gradient” expressed in PP time,
- the PS “gradient” expressed in PS time.
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- determining a first estimation of at least one combination of physical quantities of the model from the data expressed in a first time scale;
- determining at least a second estimation of the combination from the data expressed in at least a second time scale (if it is desired, during the joint inversion, to invert data expressed in x time scales, the combination has to be estimated from each of these x data or a common combination has to be estimated for each pair of time scales considered);
- carrying out an analysis of the estimations to determine at least one scale factor allowing establishing a match between the first time scale and the second time scale; and
- performing, in order to construct the representative model, the joint inversion procedure by minimizing a cost function wherein the scale factor allows expressing the synthetic data associated with the current model of the inversion described in a time scale, in another time scale, so as to evaluate a difference between these synthetic data and the data expressed in the other time scale.
mPP is the current model representative of the subsoil domain studied. It is described by the three parameters, P and S impedances and density (Ip PP, Is PP, ρPP) and it is expressed in PP time; exponent PP indicates that the model is estimated from the inversion of the PP data. For a given incidence angle θ, Rθ PP, wθ PP and Dθ PP are respectively the series of reflection coefficients (conventionally the Zoeppritz formulation or one of its approximations) corresponding to the current model, for the given angle θ, the wavelet previously estimated by well-seismics calibration of the PP seismic data associated with angle θ, and the PP seismic data associated with angle θ. mprior PP, Cd PP and Cm PP are respectively the PP a priori model and the covariance operators describing the uncertainties respectively on the PP data and the PP a priori model.
- the first term of this cost function measures the difference between the PP synthetic data corresponding to the current model mPP and the PP observed data, in the sense of the inverse of covariance matrix Cd PP,
- the second term of this cost function measures the difference between the current model and the a priori model mprior PP, in the sense of the inverse of covariance matrix Cm PP.
Knowledge of the scale factor allows the PP times to be converted to PS times and vice versa.
- the Is PP(tPP), Is PS(tPS) data that are to be matched represent here the same physical quantity,
- the Is PP(tPP), Is PS(tPS) data result from prestack stratigraphic inversions and therefore contain much less noise than the initial seismic data,
- in the single-component stratigraphic inversion methodology of Tonellot et al. (2001), the preliminary well-seismics calibration stage allowing determination of a wavelet per angle, for each type of seismic data (PP and PS), allows to best limit the phase mismatches between the two impedances to be associated in time.
where mLF corresponds to m converted to PS time via the optimum low-frequency scale factor ηLF obtained in
- the first term measures the difference between the PP synthetic data corresponding to the current model and the PP observed data, in the sense of the inverse of covariance matrix Cd PP,
- the second term measures the difference between the PS synthetic data corresponding to the current model m converted to PS time via scale factor ηLF and the PS observed data, in the sense of the inverse of covariance matrix Cd PS,
- the third term measures the difference between current model m and multiparameter a priori model mprior PP, in the sense of the inverse of covariance matrix Cm PP.
- mpp: constructed model representative of a heterogeneous medium
- JI: procedure of joint inversion
- Dθ pp: data expressed in a first time scale
- Dθ pp: data expressed in a second time scale
- ηLF: a low frequency scale factor
- J: cost function wherein Iθ pp, Is pp, ppp is first estimation of a combination of physical quantities of the model from the data expressed in a first time scale and
- Iθ ps is a second estimation of a combination of physical quantities of the model from the data expressed in a second time scale
- Dθ pp(mpp) and Dθ ps(mpp) are the synthetic data associated with the current model with the following equalities applying:
D θ pp(m pp)=R θ pp(m)*w θ pp
D θ ps(m pp)=R θ ps(m)*w θ ps
For a given angle of incidence θ, Rθ pp are the reflection coefficients, wθ pp is the wavelet previously estimated by the well seismic calibration of the PP seismic data associated with the angle θ and Dθ pp are the aforementioned first time scale data.
Claims (13)
Applications Claiming Priority (3)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
FR0408517A FR2873823B1 (en) | 2004-08-02 | 2004-08-02 | METHOD FOR CONSTRUCTING A MODEL OF A HETEROGENEOUS ENVIRONMENT DESCRIBED BY MULTIPLE PARAMETERS FROM DATA EXPRESSED IN DIFFERENT TIME SCALES |
FR0408517 | 2004-08-02 | ||
FR04/08.517 | 2004-08-02 |
Publications (2)
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US20060023569A1 US20060023569A1 (en) | 2006-02-02 |
US7701804B2 true US7701804B2 (en) | 2010-04-20 |
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US11/194,528 Expired - Fee Related US7701804B2 (en) | 2004-08-02 | 2005-08-02 | Method and constructing a model of a heterogeneous medium described by several parameters from data expressed in different time scales |
Country Status (6)
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US (1) | US7701804B2 (en) |
EP (1) | EP1624321B1 (en) |
CN (1) | CN1734288B (en) |
CA (1) | CA2514112A1 (en) |
FR (1) | FR2873823B1 (en) |
NO (1) | NO333842B1 (en) |
Cited By (1)
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US20120143575A1 (en) * | 2009-10-23 | 2012-06-07 | Matthias Imhof | Method For Optimization With Gradient Information |
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-
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- 2005-07-28 CA CA002514112A patent/CA2514112A1/en not_active Abandoned
- 2005-07-28 EP EP05291620A patent/EP1624321B1/en not_active Expired - Fee Related
- 2005-07-29 NO NO20053685A patent/NO333842B1/en not_active IP Right Cessation
- 2005-08-02 US US11/194,528 patent/US7701804B2/en not_active Expired - Fee Related
- 2005-08-02 CN CN2005100885862A patent/CN1734288B/en not_active Expired - Fee Related
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Cited By (2)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US20120143575A1 (en) * | 2009-10-23 | 2012-06-07 | Matthias Imhof | Method For Optimization With Gradient Information |
US8855987B2 (en) * | 2009-10-23 | 2014-10-07 | Exxonmobil Upstream Research Company | Method for optimization with gradient information |
Also Published As
Publication number | Publication date |
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CN1734288A (en) | 2006-02-15 |
US20060023569A1 (en) | 2006-02-02 |
NO20053685L (en) | 2006-02-03 |
FR2873823B1 (en) | 2006-09-15 |
NO20053685D0 (en) | 2005-07-29 |
EP1624321A1 (en) | 2006-02-08 |
NO333842B1 (en) | 2013-09-30 |
CA2514112A1 (en) | 2006-02-02 |
CN1734288B (en) | 2010-05-05 |
EP1624321B1 (en) | 2007-03-28 |
FR2873823A1 (en) | 2006-02-03 |
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